Jawa asked me this in a comment and I didn't know the answer. So I present it to the meta SO community:

[To get the Yearling badge] Do you need to earn the 200 rep within that one year or is it enough to get 200 at some point after being a member for a year? And does 'a year' mean the very first 12 months or the last (sliding window of) 12 months?

I would assume that if you hit 200 reputation after you've already been around for a year, then you would get the Yearling badge. But I don't know.